from timeit import Timer

import sys
import math


def Problem():
    """By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

        3
        7 5
        2 4 6
        8 5 9 3
        
        That is, 3 + 7 + 4 + 9 = 23.
        
        Find the maximum total from top to bottom of the triangle below:
        
        75
        95 64
        17 47 82
        18 35 87 10
        20 04 82 47 65
        19 01 23 75 03 34
        88 02 77 73 07 63 67
        99 65 04 28 06 16 70 92
        41 41 26 56 83 40 80 70 33
        41 48 72 33 47 32 37 16 94 29
        53 71 44 65 25 43 91 52 97 51 14
        70 11 33 28 77 73 17 78 39 68 17 57
        91 71 52 38 17 14 91 43 58 50 27 29 48
        63 66 04 68 89 53 67 30 73 16 69 87 40 31
        04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
        
    NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)
    """

    #print it
    def printTriangle(t):
        l = len(t) * 2
        for r in t:
            s =  " ".center(l - len(r)*2)
            print
            print s,
            for p in r:
                print str(p).center(2), " ",
        print
    
    triangle = """75
        95 64
        17 47 82
        18 35 87 10
        20 04 82 47 65
        19 01 23 75 03 34
        88 02 77 73 07 63 67
        99 65 04 28 06 16 70 92
        41 41 26 56 83 40 80 70 33
        41 48 72 33 47 32 37 16 94 29
        53 71 44 65 25 43 91 52 97 51 14
        70 11 33 28 77 73 17 78 39 68 17 57
        91 71 52 38 17 14 91 43 58 50 27 29 48
        63 66 04 68 89 53 67 30 73 16 69 87 40 31
        04 62 98 27 23 09 70 98 73 93 38 53 60 04 23"""
    
    #Get proper triangle
    triangle = triangle.splitlines()
    triangle = map(lambda x: x.strip().split(" "), triangle)
    triangle = map(lambda x: map(int, x), triangle)
    
    printTriangle(triangle)
    
    
    ## Calculate ##
    
    #memorize the sub triangle max sum
    maxsum = triangle[len(triangle)-2][:]
    
    #Start with second last 
    for r in xrange(len(triangle)-2, -1, -1):
        for p in xrange(0, len(triangle[r])):
            
            if triangle[r+1][p] > triangle[r+1][p+1]:
                triangle[r][p] += triangle[r+1][p]
            else:
                triangle[r][p] += triangle[r+1][p+1]
    
        
    ans = triangle[0][0]

    
    print "Answer for Problem 18 = %s " % (ans,)




    
if __name__ == "__main__":
    t = Timer(setup='from __main__ import Problem', stmt='Problem()').timeit(1)
    print "Execution time = %0.3f seconds" %(t,)